##The sum of the squares of the first ten natural numbers is,
##12 + 22 + ... + 102 = 385
##The square of the sum of the first ten natural numbers is,
##(1 + 2 + ... + 10)2 = 552 = 3025
##Hence the difference between the sum of the squares of the first ten
##natural numbers and the square of the sum is 3025  385 = 2640.
##Find the difference between the sum of the squares of the first one hundred
##natural numbers and the square of the sum.
def f(n):
    return sum(range(1,n+1))**2-sum(i**2 for i in range(1,n+1))
def f2(n):
    return ((n+1)*n*(n-1)*(3*n+2))//12
print(f2(100))
